| Structural design under seismic load requires proper consideration of uncertainties associated with loads and resistance as well as the limited ability of analytical models to describe the response of a structure. To account for these uncertainties, the design parameters in current seismic codes need to be calibrated based on required safety and satisfactory performance under future earthquakes in terms of reliability. The calibration is done by minimization of the difference between actual and target probabilities for both serviceability and ultimate limit states. The Response Surface Method (RSM) with a central composite design is used to expedite the calibration process. Since information is required on the actual probabilities of exceeding various limit state conditions for various structural configurations which typically requires a large number of nonlinear time history structural response analyses, an Equivalent Nonlinear System (ENS) is used to replace the MDOF analytical model. The ENS retains the important properties of the original system, i.e., the dynamic characteristics of the first two modes, the global yield displacement and post-yielding behavior of the structure. Response scaling factors based on extensive regression analyses of structures of up to 12 stories under historical earthquakes are then applied to the responses calculated using the ENS in order to obtain responses comparable to the original structure. Numerical examples on the calibration are given, and parametric studies are carried out to show the dependence of the structural design parameters on the target reliabilities for both serviceability and ultimate limit states. The computational advantage and the accuracy of the proposed methods are also shown. |
